CHICAGO – Taj Gibson tried to answer the first question with a straight face, and failed miserably. Four or five words in, his smile broke through the clouds and spread ear to ear.

From there, the Chicago Bulls forward’s expression told the tale. While he dressed after is team’s 93-87 victory over Sacramento Wednesday at United Center, his agent, Mark Bartelstein, was upstairs with Bulls management. The business at hand: Crossing T’s and dotting I’s on a four-year contract extension worth $38 million, about 50 minutes before the NBA deadline for such deals.

“This is where I want to be,” Gibson said. “Both sides just came together and got it done.”

He added: “I didn’t want to go through [the season without a deal]. To turn down, that’s a lot of money. Especially for the security. I’m relieved.”

Four hours earlier, Gibson looked despondent. The gap in the negotiations was too great, and the fourth-year forward from USC doubted whether it would get done at all. It nagged at him a little as he played — four blocked shots but modest otherwise, with four points and five rebounds in 19 minutes. Then the horn blew, the Bulls won and Gibson knew that the 11 p.m. CT cutoff was fast approaching.

That’s when Bulls GM Gar Forman and VP John Paxson sought him out again and told Gibson they wanted him around for a long time. Gibson told them, hey, he wanted to retire in Chicago. After that, it was up to the bosses and Bartelstein.

“It kind of dawned on me,” said Gibson, a valuable defender and reserve who will log starter’s minutes in 2012-13. “When you’re put in that position, it’s hard. It’s hard turning down that much money, knowing you have to go through a whole season without injuries. … Night in, night out, never knowing what can happen.”

The Bulls were determined not to add another eight-figure annual salary to their payroll (they already have four for next season). Gibson – who has averaged 12.3 points, 9.6 rebounds and 2.0 blocked per 36 minute played in three seasons – and Bartelstein knew the market that produced deadline-day deals of $44 million for Golden State’s Stephen Curry and $40 million for Toronto’s DeMar DeRozan.

They also knew the pros and cons of waiting for Gibson’s restricted free agency next July. The idea that Gibson, who had a rough, disadvantaged upbringing in Brooklyn, could turn down tens of millions of dollars …

“Mark was real with me. He said, ‘I don’t want you to turn this down,’ ” Gibson said. “He said, ‘I know we can probably get more this summer. But it’s all about if you’re happy or not.’

“You do want to see what else is out there, but you don’t want to be in some hellhole somewhere just chasing the bucks.”

That won’t happen now. Gibson is happy, the Bulls are happy and the other players, who teased him about picking up the check for dinner, are happy too.

“That’s my young boy. He’s my rookie, in this life and the next life,” Bulls center Joakim Noah said. “It’s well deserved. I see Taj’s grind every day. I know how much he fights every night. I’ve been through it, so I know it’s an unbelievable feeling.”